3688544715 - Tutorial questions: Chapter 5 EX1. Determine...

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Tutorial questions: Chapter 5 EX1. Determine the types of the following PDEs (a) (b) Ans. (a) Parabolic PDE. (b) Elliptic PDE EX2. Calculate the partial differentiation of the following function x T k t T 2 2 = 0 2 2 2 2 = + y T x T 2 2 2 ) , , ( z y x z y x u + + = Ans . 6 2 = u z u y u x u u 2 2 2 2 2 2 2 + + =
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EX3. Verify by direct substitution that is a solution to the heat transfer equation for any integer n=1, 2, 3, … t kn e x n t x T 2 2 ) sin( ) , ( π = 2 2 x T k t T =
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EX4. . Verify by calculating using the forward different method and using the central different method that the temperatures listed in the table below are solutions to the heat transfer equation at time t=0.02 t T / 2 2 / x T 2 2 x T t T = 0.0 0.40 0.64 0.64 0.40 0.0 t=0.04 0.0 0.48 0.80 0.80 0.48 0.0 t=0.02 0.0 0.64 0.96 0.96 0.64 0.0 t=0 x 6 =1.0 x 5 =0.8 x 4 =0.6 x 3 =0.4 x 2 =0.2 x 1 =0
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EX5. Establish a PDE, initial condition and
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3688544715 - Tutorial questions: Chapter 5 EX1. Determine...

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